Least-Squares Regression

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Least-Squares Regression Ekran Görüntüsü  İndir  Göm(Embed)
  • Linear Regression
  • İlinti
  • Residuals

İçerik

  • Linear Regression
  • İlinti
  • Residuals
  • Outlier
  • Data

Description

Create your own scatter plot or use real-world data and try to fit a line to it! Explore how individual data points affect the correlation coefficient and best-fit line.

Örnek Öğrenim Hedefleri

  • Interpret r (the correlation coefficient) as data points are added, moved, or removed.
  • Interpret the sum of the squared residuals while manually fitting a line.
  • Interpret the sum of the squared residuals of a best-fit line as a data point is added, moved, or removed.
  • Compare the sum of the squared residuals between a manually fitted line and the best-fit line.
  • Determine if a linear fit is appropriate.

Standards Alignment

Common Core - Math

8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.A.2
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
HSS-ID.B.6
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
HSS-ID.B.6a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
HSS-ID.B.6b
Informally assess the fit of a function by plotting and analyzing residuals.
HSS-ID.B.6c
Fit a linear function for a scatter plot that suggests a linear association.
HSS-ID.C.8
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Version 1.1.18

Teacher Tips

Öğretmen el kitabı (pdf) Phet ekibi tarafından oluşturulan ipuçları içerir. ( PDF ).

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Teacher-Submitted Activities

Preguntas de razonamiento para todas las simulaciones HTML5 A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Bu katkı PhET tarafından tasarlanmıştır. Diana López Mezun
Lisans-İleri
Lİse
K-5
Ortaokul
Lisans-Giriş
Discuss
Ödev
Astronomi
Fizik
Kimya
Matematik
Middle School Math Sim Alignment Bu katkı PhET tarafından tasarlanmıştır. Amanda McGarry Ortaokul Diğer Matematik
Alignment of PhET sims with NGSS Bu katkı PhET tarafından tasarlanmıştır. Trish Loeblein Lİse Diğer Yer Bilimleri
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How do PhET simulations fit in my middle school program? Bu katkı PhET tarafından tasarlanmıştır. Sarah Borenstein Ortaokul Diğer Biyoloji
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Yer Bilimleri
Fizik
Mapping of PhET and IBDP Physics Jaya Ramchandani Lİse Diğer Fizik
MS and HS TEK to Sim Alignment Elyse Zimmer Ortaokul
Lİse
Diğer Fizik
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PhET Simulations Aligned for AP Physics C Roberta Tanner Lİse Diğer Fizik
Understanding Line of best fit and Correlation Coefficient Rebecca Battat Lİse Guided Matematik
Data Detective Kelly Findley, Mary Burr Ortaokul Guided Matematik
Correlation vs Causation Andy Braaten Lİse
Lisans-Giriş
Laboratuvar Matematik

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The new HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iPad:
iOS 11+ Safari
iPad compatible sims

Android:
Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Chromebook:
Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge and Internet Explorer 11, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.9.5+, Safari 9+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

Tasarım Ekibi Harici Kütüphaneler Sayesinde
  • Amanda McGarry (lead)
  • Martin Veillette (developer)
  • Patricia Loeblein
  • Ariel Paul
  • Kathy Perkins
  • almond-0.2.9.js
  • easing-equations-r12
  • FileSaver-b8054a2.js
  • fontawesome-webfont-3.0.2.svg
  • jama-1.0.2
  • jquery-2.1.0.js
  • lodash-2.4.1.js
  • pegjs-0.7.0.js
  • seedrandom-2.4.2.js
  • text-2.0.12.js
  • Tween-r12.js